question_answer

A man on the top of a bamboo pole observes that the angles of depression of the base and the top of another pole are \[60{}^\circ \] and \[30{}^\circ \] respectively. If the second pole stands 5 m above the ground level, then the height of the bamboo, on which the man is sitting, is

A)  5 m                       

B)         7.5 m  

C)  10 m                    

D)         12.5 m

Correct Answer: B

Solution :

From \[\Delta \,BMQ,\]                 \[x=y\,\cot \,{{30}^{o}}=\sqrt{3}y\]         ??(i) From \[\Delta \,APQ,\]  \[x=(y+5)\,\cot {{60}^{o}}\] or            \[x=\frac{1}{\sqrt{3}}(y+5)\]                       ?..(ii) From equations (i) and (ii), we have                 \[\sqrt{3}y=\frac{(y+5)}{\sqrt{3}}\] or            \[y=2.5\] \[\therefore \] Height of bamboo pole \[=PQ=PM+MQ\]                 \[=5+2.5\]                 \[=7.5\,m\]